course phy232
Problem 14.45:The upper edge of a gate in a dam runs along the water surface. The gate is 2.00 m high and 4.00m wide and is hinged along a horizontal line through its center. Calculate the torque about the hinge arising from the force due to the water.
Well, we need to find the force of the water of the water on the gate. The first step I did was find the area of the gate, which was 8.00 m^2. I took the pressure to be (1000kg/m^3)(9.81m/2^2)(d'h) (Am I making the correct assumption that the pressure is going to vary with the height of the water on the dam?).
Using calculus we can conclude that the force on slice will be the area (8.00m^2)(1000kg?m^3)(9.81m/s^2)(d'h)(hi)
then times the moment arm 4.0m, which will can integrate from 2 to 0 (relative to the height of the water)?
You need to find the area of a strip of width `dh at depth h; then find the force exerted by pressure on this strip, and finally the torque exerted byt he strip.
Problem 14.51:
A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the tube until the vertical height of the water column is 15.0cm.
A.) What is the gauge pressure at the water-mercury interface?
The gauge pressure at the interface will be the pressure of the water, which is (1000kg/m^3)(9.81m/s^2)(.15m)= 1471.5 Pa
not so because the mercury will move in response to the pressure of the water, leaving less than 15 cm of water above the interface
B.) Calculate the vertical distance h from the top of the mercury in the right-hand arm of the tube to the top of the water in the left-hand arm.
This is where I was a little confused: I was thinking that you can use energy considerations on this possible?
my previous note applies here as well